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arXiv · 2102.04713

Two kinds of real lines on real del Pezzo surfaces of degree 1

Sergey Finashin·Viatcheslav Kharlamov
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Abstract

We show how the real lines on a real del Pezzo surface of degree 1 can be split into two species, elliptic and hyperbolic, via a certain distinguished, intrinsically defined, Pin-structure on the real locus of the surface. We prove that this splitting is invariant under real automorphisms and real deformations of the surface, and that the difference between the total numbers of hyperbolic and elliptic lines is always equal to 16.

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Sergey Finashin, Viatcheslav Kharlamov. 2021-02-09. Two kinds of real lines on real del Pezzo surfaces of degree 1. https://arxiv.org/abs/2102.04713

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